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Add parentheses
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aisejohan committed Dec 10, 2019
1 parent 248d7eb commit cf2e8d0
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Expand Up @@ -96,6 +96,7 @@ Dragos Fratila
Robert Friedman
Robert Furber
Ofer Gabber
Juan Sebastian Gaitan
Lennart Galinat
Martin Gallauer
Luis Garcia
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4 changes: 2 additions & 2 deletions brauer.tex
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Expand Up @@ -221,10 +221,10 @@ \section{Lemmas on algebras}
W/(V' \otimes_k K) \subset (V/V') \otimes_k K.
$$
If $\overline{v} \in V/V'$ is a nonzero vector such that
$\overline{v} \otimes 1$ is contained in $W/V' \otimes_k K$,
$\overline{v} \otimes 1$ is contained in $W/(V' \otimes_k K)$,
then we see that $v \otimes 1 \in W$ where $v \in V$ lifts $\overline{v}$.
This contradicts our construction of $V'$. Hence we may replace
$V$ by $V/V'$ and $W$ by $W/V' \otimes_k K$ and it suffices to prove
$V$ by $V/V'$ and $W$ by $W/(V' \otimes_k K)$ and it suffices to prove
that $W \cap (V \otimes 1)$ is nonzero if $W$ is nonzero.

\medskip\noindent
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